A355464 Expansion of Sum_{k>=0} x^k/(1 - k^k * x)^(k+1).

1, 2, 4, 17, 210, 9217, 1399298, 811229225, 2071392232962, 20710319937493889, 1137259214532706572162, 255141201504146525745627265, 348787971214016591166179037803522, 2262996819897931095524655885144485185409

Offset: 0

Author

Seiichi Manyama, Jul 03 2022

Keywords

• nonn

Crossrefs

Cf. A086331, A320287, A349893, A355440, A355463.

Cf. A000248, A135746, A355473.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-k^k*x)^(k+1)))

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, exp(k^k*x)*x^k/k!)))

PARI

a(n) = sum(k=0, n, k^(k*(n-k))*binomial(n, k));

Formula

E.g.f.: Sum_{k>=0} exp(k^k * x) * x^k/k!.

a(n) = Sum_{k=0..n} k^(k*(n-k)) * binomial(n,k).